mary has a solution that is 60% alcohol and another that is 20% alcohol. how much of each should she use to make 100 milliliters of a solution that is 52% alcohol?

Question

please help, I don't understand how to do this problem!

Answer 1

Let's say Mary used X ml of the 60% solution and Y ml of the 20% solution. You have two requirements:

X + Y = 100 (the total amount needed), and

0.6X + 0.2Y = 52 (the amount of a alcohol in the final mixture)

Solve those two equations in two unknowns. One way to do that would be to substitute 100 - X for Y in the second equation.
0.6X + 20 -0.2X = 52
0.4X = 32
etc